Discrete Mathematics Partial Orderings Online Exam Quiz
Discrete Mathematics Partial Orderings GK Quiz. Question and Answers related to Discrete Mathematics Partial Orderings. MCQ (Multiple Choice Questions with answers about Discrete Mathematics Partial Orderings
The inclusion of ______ sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.
Options
A : {1}, {2, 4}
B : {1}, {1, 2, 3}
C : {1}
D : {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}
Consider the ordering relation a | b ? N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________
Options
A : | is an equivalence relation
B : It is a total order
C : Every subset of N has an upper bound under |
D : (N,|) is a lattice but not a complete lattice
Suppose X = {a, b, c, d} and ?1 is the partition of X, ?1 = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by __________
Options
A : 15
B : 10
C : 34
D : 5
Let a set S = {2, 4, 8, 16, 32} and <= be the partial order defined by S <= R if a divides b. Number of edges in the Hasse diagram of is ______
Options
A : 6
B : 5
C : 9
D : 4
Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true?
Options
A : Every non-empty subset of has a greatest lower bound
B : It is uncountable
C : Every non-empty finite subset of has a least upper bound
D : Every non-empty subset of has a least upper bound
If the longest chain in a partial order is of length l, then the partial order can be written as _____ disjoint antichains.
Options
A : l2
B : l+1
C : l
D : ll
A partial order ? is defined on the set S = {x, b1, b2, … bn, y} as x ? bi for all i and bi ? y for all i, where n ? 1. The number of total orders on the set S which contain the partial order ? is ______
Options
A : n+4
B : n2
C : n!
D : 3
The less-than relation, <, on a set of real numbers is ______
Options
A : not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
B : a partial ordering since it is asymmetric and reflexive
C : a partial ordering since it is antisymmetric and reflexive
D : not a partial ordering because it is not antisymmetric and reflexive
Let (A, ?) be a partial order with two minimal elements a, b and a maximum element c. Let P:A –> {True, False} be a predicate defined on A. Suppose that P(a) = True, P(b) = False and P(a) ? P(b) for all satisfying a ? b, where ? stands for logical implication. Which of the following statements cannot be true?
Options
A : P(x) = True for all x S such that x ? b
B : P(x) = False for all x ? S such that b ? x and x ? c
C : P(x) = False for all x ? S such that x ? a and x ? c
D : P(x) = False for all x ? S such that a ? x and b ? x
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